# Trouble transforming a groebner basis

I'm using sage to compute Gröbner bases (in lexicographic order) over a fractional field. This has been working out well so far. For computational efficiency I've read that degrevlex order is often preferred for the initial basis calculation, followed by a transformation (using the FGLM algorithm) to the desired order (lex in my case).

However, I'm facing a problem when I try to transform the basis, my invocation might be wrong, but currently this is yielding me a TypeError: no conversion to a Singular ring defined.

This is the .sage file:

P.<p0, p1, p2, p3, p4, p5, p6, p7, p8, p9> = PolynomialRing(QQ)
F = Frac(P)
R = PolynomialRing(F, order='degrevlex', names=('z0', 'z1', 'z2', 'z3', 'z4', 'z5', 'z6', 'z7'))
(z0, z1, z2, z3, z4, z5, z6, z7,) = R._first_ngens(8)

I = R.ideal(p0*z0*z1 - z2*z3, p1*z4 - z3*z5, p2*z1*z5 - z6, -p3 - p4 - p5 + z4 + z5 + z6, -p5 - p6 - p7 + z0 + z3 + z4, -p3 - p8 - p9 + z1 + z2 + z6, -p7 - p8 + z0 + z2, -z6 + z7)
gb = I.groebner_basis()
print('So far so good...')
S = PolynomialRing(F, order='lex', names=('z0', 'z1', 'z2', 'z3', 'z4', 'z5', 'z6', 'z7'))
gbasis = Ideal(gb).transformed_basis('fglm', S)

print([{k: str(v) for k, v in _.dict().items()} for _ in gbasis])

and this is my backtrace:

So far so good...
Traceback (most recent call last):
File "sage/rings/polynomial/multi_polynomial_libsingular.pyx", line 1222, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._singular_ (build/cythonized/sage/rings/polynomial/multi_polynomial_libsingular.cpp:13949)
ValueError

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
File "/tmp/tmp8h3xz_3s.sage.py", line 16, in <module>
gbasis = Ideal(gb).transformed_basis('fglm', S)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3/dist-packages/sage/rings/polynomial/multi_polynomial_ideal.py", line 297, in __call__
return self.f(self._instance, *args, **kwds)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3/dist-packages/sage/rings/qqbar_decorators.py", line 96, in wrapper
return func(*args, **kwds)
^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3/dist-packages/sage/interfaces/singular.py", line 2763, in wrapper
return func(*args, **kwds)
^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3/dist-packages/sage/libs/singular/standard_options.py", line 142, in wrapper
return func(*args, **kwds)
^^^^^^^^^^^^^^^^^^^
File "/usr/lib/python3/dist-packages/sage/rings/polynomial/multi_polynomial_ideal.py", line 2055, in transformed_basis
Rs = singular(R)
^^^^^^^^^^^
File "/usr/lib/python3/dist-packages/sage/interfaces/singular.py", line 766, in __call__
return x._singular_(self)
^^^^^^^^^^^^^^^^^^
File "sage/rings/polynomial/multi_polynomial_libsingular.pyx", line 1236, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._singular_ (build/cythonized/sage/rings/polynomial/multi_polynomial_libsingular.cpp:14457)
File "sage/rings/polynomial/multi_polynomial_libsingular.pyx", line 1433, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._singular_init_ (build/cythonized/sage/rings/polynomial/multi_polynomial_libsingular.cpp:16290)
TypeError: no conversion to a Singular ring defined

Any clue as to what I might be doing wrong?

I'm using sage 9.5, provided by Debian 12 (bookworm)

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You can use Singular's notion of a ring with parameters, but Sage's PolynomialRing interface to Singular doesn't understand this yet, so currently you have to do it by hand like so:

R = singular.ring('(0, p0, p1, p2, p3, p4, p5, p6, p7, p8, p9)', '(z0, z1, z2, z3, z4, z5, z6, z7)', 'dp')
I = singular.ideal('p0*z0*z1 - z2*z3', 'p1*z4 - z3*z5', 'p2*z1*z5 - z6', '-p3 - p4 - p5 + z4 + z5 + z6', '-p5 - p6 - p7 + z0 + z3 + z4', '-p3 - p8 - p9 + z1 + z2 + z6', '-p7 - p8 + z0 + z2', '-z6 + z7')
singular.option('redSB')
gb = singular.std(I)
S = singular.ring('(0, p0, p1, p2, p3, p4, p5, p6, p7, p8, p9)', '(z0, z1, z2, z3, z4, z5, z6, z7)', 'lp')
J = singular.ideal('fglm({}, {})'.format(R.name(), gb.name()))
J

It takes a few minutes but finally returns:

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z6-z7,
...

Better yet would be using the libSingular interface.

more

Thank you so much Ricardo. Regarding your note about using libSingular: Am I interpreting the situation correctly if I'm guessing that it would enable a more natural usage from sage, whereas the code you provide here are interactive singular commands sent to a console session? But performance would be the same, no?

( 2023-07-30 18:23:18 +0100 )edit
1

You're welcome! Indeed it wouldn't make a difference in performance, it would just be cleaner than using the pexpect interface. As for more natural usage from Sage, you could take your originally defined ring and ideal, and create the corresponding Singular objects e.g. by string manipulation.

( 2023-07-30 20:31:07 +0100 )edit
1

@rburing, just FYI, I opened an issue relating to converting back the polynomias to Sage using ._sage_()here: https://github.com/sagemath/sage/issu...

( 2023-07-30 21:08:40 +0100 )edit

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Last updated: Jul 30 '23